Let ∑ is contained in P~4 be an integral hypersurface of degree s with a (s - 2)-uple plane. We show that the degrees of smooth surfaces S is contained in ∑ with q(S) = 0 are bounded by a function of s. We also show that if 5 is contained in P~4 is a smooth surface with q(S) = 0 and if S lies on a quartic hypersurface ∑ such that dim(Sing(∑)) = 2, then deg(S) ≤ 40.
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